Question

Find the equation of the straight line which passes through the point (2, 3) and makes intercepts equal in magnitude but opposite in sign on the axes.​

Answer 1

EXPLANATION.

→ equation of the straight line passes through

the point (2,3) and makes the intercept

equal in magnitude but opposite in sign

on the axes.

→ x/a + y/a = 1

→ Case = 1.

→ x/-a + y/a = 1

→ y - x = a

→ Line passes through point (2,3)

→ 3 - 2 = a

→ a = 1

→ Equation = y - x = 1

→ Case = 2.

→ x/a + y/-a = 1

→ x - y = a

→ 2 - 3 = a

→ a = -1.

→ Equation = x - y = -1.

Answer 2

$\mathtt{\huge{\underline{\bf{\red{Given :-}}}}}$

• The straight line which passes through the point (2, 3).

• It makes intercepts equal in magnitude but opposite in sign on the axes.

$\mathtt{\huge{\underline{\bf{\green{To\:Find :-}}}}}$

• The equation of the straight line.

$\mathtt{\huge{\underline{\bf{\pink{Solution :-}}}}}$

★ A line which can be extended from both sides without making any curves till infinity is called a straight line.

General equation of straight line

• ax + by + c = 0

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Using,

$\dfrac{x}{a} + \dfrac{y}{a} = 1$

According to the question,

It makes intercepts equal in magnitude but opposite in sign on the axes.

For Equation 1 :-

$\dfrac{x}{-a} + \dfrac{y}{a} = 1$

➝ $\dfrac{ y - x}{a} = 1$

➝ y - x = a

➝ a = y - x .......(a)

The straight line passes through the point (2, 3).

➝ a = 3 - 2

➝ a = 1 .........(b)

Comparing equation a & b ,

➝ y - x = 1

➝ - x + y = 1

For Equation 2 :-

$\dfrac{x}{a} + \dfrac{y}{-a} = 1$

➝ $\dfrac{ x - y }{a} = 1$

➝ x - y = a

➝ a = x - y .......( k )

The straight line passes through the point (2, 3).

➝ a = 2 - 3

➝ a = - 1 .........(l)

Comparing equation k & l ,

➝ x - y = 1

➝ x - y = - 1

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